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Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 24, 144, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6}*576a
   3-fold quotients : {2,6,12}*384a
   4-fold quotients : {2,6,12}*288b, {2,6,3}*288
   6-fold quotients : {2,6,6}*192
   8-fold quotients : {2,6,6}*144b
   12-fold quotients : {2,2,12}*96, {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,6,3}*72
   24-fold quotients : {2,3,3}*48, {2,2,6}*48
   36-fold quotients : {2,2,4}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)
( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)
( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)( 80, 81)
( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)( 93,104)
( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)(120,121)
(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)
(131,143)(132,145)(133,144)(134,146);;
s2 := (  3, 15)(  4, 16)(  5, 18)(  6, 17)(  7, 23)(  8, 24)(  9, 26)( 10, 25)
( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 29, 30)( 31, 35)( 32, 36)( 33, 38)
( 34, 37)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)( 45, 62)
( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 65, 66)( 67, 71)( 68, 72)
( 69, 74)( 70, 73)( 75,123)( 76,124)( 77,126)( 78,125)( 79,131)( 80,132)
( 81,134)( 82,133)( 83,127)( 84,128)( 85,130)( 86,129)( 87,111)( 88,112)
( 89,114)( 90,113)( 91,119)( 92,120)( 93,122)( 94,121)( 95,115)( 96,116)
( 97,118)( 98,117)( 99,135)(100,136)(101,138)(102,137)(103,143)(104,144)
(105,146)(106,145)(107,139)(108,140)(109,142)(110,141);;
s3 := (  3, 82)(  4, 80)(  5, 81)(  6, 79)(  7, 78)(  8, 76)(  9, 77)( 10, 75)
( 11, 86)( 12, 84)( 13, 85)( 14, 83)( 15,106)( 16,104)( 17,105)( 18,103)
( 19,102)( 20,100)( 21,101)( 22, 99)( 23,110)( 24,108)( 25,109)( 26,107)
( 27, 94)( 28, 92)( 29, 93)( 30, 91)( 31, 90)( 32, 88)( 33, 89)( 34, 87)
( 35, 98)( 36, 96)( 37, 97)( 38, 95)( 39,118)( 40,116)( 41,117)( 42,115)
( 43,114)( 44,112)( 45,113)( 46,111)( 47,122)( 48,120)( 49,121)( 50,119)
( 51,142)( 52,140)( 53,141)( 54,139)( 55,138)( 56,136)( 57,137)( 58,135)
( 59,146)( 60,144)( 61,145)( 62,143)( 63,130)( 64,128)( 65,129)( 66,127)
( 67,126)( 68,124)( 69,125)( 70,123)( 71,134)( 72,132)( 73,133)( 74,131);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)
( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)
( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)
( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)
( 80, 81)( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)
( 93,104)( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)
(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)
(130,142)(131,143)(132,145)(133,144)(134,146);
s2 := Sym(146)!(  3, 15)(  4, 16)(  5, 18)(  6, 17)(  7, 23)(  8, 24)(  9, 26)
( 10, 25)( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 29, 30)( 31, 35)( 32, 36)
( 33, 38)( 34, 37)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)
( 45, 62)( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 65, 66)( 67, 71)
( 68, 72)( 69, 74)( 70, 73)( 75,123)( 76,124)( 77,126)( 78,125)( 79,131)
( 80,132)( 81,134)( 82,133)( 83,127)( 84,128)( 85,130)( 86,129)( 87,111)
( 88,112)( 89,114)( 90,113)( 91,119)( 92,120)( 93,122)( 94,121)( 95,115)
( 96,116)( 97,118)( 98,117)( 99,135)(100,136)(101,138)(102,137)(103,143)
(104,144)(105,146)(106,145)(107,139)(108,140)(109,142)(110,141);
s3 := Sym(146)!(  3, 82)(  4, 80)(  5, 81)(  6, 79)(  7, 78)(  8, 76)(  9, 77)
( 10, 75)( 11, 86)( 12, 84)( 13, 85)( 14, 83)( 15,106)( 16,104)( 17,105)
( 18,103)( 19,102)( 20,100)( 21,101)( 22, 99)( 23,110)( 24,108)( 25,109)
( 26,107)( 27, 94)( 28, 92)( 29, 93)( 30, 91)( 31, 90)( 32, 88)( 33, 89)
( 34, 87)( 35, 98)( 36, 96)( 37, 97)( 38, 95)( 39,118)( 40,116)( 41,117)
( 42,115)( 43,114)( 44,112)( 45,113)( 46,111)( 47,122)( 48,120)( 49,121)
( 50,119)( 51,142)( 52,140)( 53,141)( 54,139)( 55,138)( 56,136)( 57,137)
( 58,135)( 59,146)( 60,144)( 61,145)( 62,143)( 63,130)( 64,128)( 65,129)
( 66,127)( 67,126)( 68,124)( 69,125)( 70,123)( 71,134)( 72,132)( 73,133)
( 74,131);
poly := sub<Sym(146)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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